Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function

Details Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function

2001-01-09

arxiv.org/abs/math/0101075v1

Mathematics

Combinatorics

Scientific paper

A partially ordered set is r-thick if every nonempty open interval contains at least r elements. This paper studies the flag vectors of graded, r-thick posets and shows the smallest convex cone containing them is isomorphic to the cone of flag vectors of all graded posets. It also defines a k-analogue of the Mobius function and k-Eulerian posets, which are 2k-thick. Several characterizations of k-Eulerian posets are given. The generalized Dehn-Sommerville equations are proved for flag vectors of k-Eulerian posets. A new inequality is proved to be valid and sharp for rank 8 Eulerian posets.

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